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Research Papers: Fundamental Issues and Canonical Flows

# Flows and Their Stability in Rotating Cylinders With a Porous Lining

[+] Author and Article Information
M. Subotic1

School of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, OK 73019

F. C. Lai

School of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, OK 73019

1

Present address: Mechanical Engineer, Schlumberger Oilfield Services, Sugar Land, TX 77478.

J. Fluids Eng 132(5), 051201 (Apr 27, 2010) (7 pages) doi:10.1115/1.4001541 History: Received March 12, 2009; Revised March 06, 2010; Published April 27, 2010; Online April 27, 2010

## Abstract

Flow fields in an annulus between two rotating cylinders with a porous lining have been numerically examined in this study. While the outer cylinder is stationary, the inner cylinder is rotating with a constant angular speed. A homogeneous and isotropic porous layer is press-fit to the inner surface of the outer cylinder. The porous sleeve is saturated with the fluid that fills the annulus. The effects of porous sleeve thickness and its properties on the flows and their stability in the annulus are numerically investigated. Three-dimensional momentum equations for the porous and fluid layers are formulated separately and solved simultaneously in terms of velocity and vorticity. The solutions have covered a wide range of the governing parameters $(10−5≤Da≤10−2, 2000≤Ta≤5000, 0.8≤b¯≤0.95)$. The results obtained show that the presence of a porous sleeve generally has a stabilizing effect on the flows in the annulus.

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## Figures

Figure 1

Flow between two rotating cylinders with a porous lining

Figure 2

Evolution of vortex patterns with the Taylor number (a¯=0.74375, L=5 and Δζ=0.2): (a) Ta=2600, (b) Ta=2800, (c) Ta=3000, and (d) Ta=3100

Figure 3

Solution path for a pure fluid flow in the rotating cylinders (a¯=0.74375 and L=5)

Figure 4

Growth rate of the relative flow intensity in the axial direction for a pure fluid flow in the rotating cylinders (a¯=0.74375 and L=5)

Figure 5

Effect of the presence of a porous sleeve on the distribution of vorticity (a¯=0.74375, b¯=0.875, L=5, ϕ=0.25, Ta=3040, and Δζ=0.2): (a) without porous sleeve, (b) Da=10−2, (c) Da=10−3, (d) Da=10−4, and (e) Da=10−5

Figure 6

Effects of the presence of a porous sleeve on the flow tangential velocity at the midsection of the annulus, Z=2.5 (a¯=0.74375, b¯=0.875, L=5, ϕ=0.25, and Ta=3040)

Figure 7

Effects of the presence of a porous sleeve on the average shear stress at the surface of the inner cylinder: (a¯=0.74375, b¯=0.875, L=5, ϕ=0.25, and Ta=3040)

Figure 8

Effect of porous sleeve thickness on the distribution of vorticity (a¯=0.74375, L=5, ϕ=0.25, Da=10−3, Ta=3040, and Δζ=0.2): (a) b¯=0.95, (b) b¯=0.9, and (c) b¯=0.85

Figure 9

Effects of porous sleeve thickness on the tangential velocity profile at the midsection of the annulus, Z=2.5 (a¯=0.74375, L=5, ϕ=0.25, Da=10−3, and Ta=3040)

Figure 10

Effects of porous sleeve thickness on the average shear stress at the surface of the inner cylinder (a¯=0.74375, L=5, ϕ=0.25, Da=10−3, and Ta=3040)

Figure 11

Development of vorticity profiles with Taylor number (Da=10−5, a¯=0.74375, b¯=0.95, L=5, ϕ=0.25 and Δζ=0.2): (a) Ta=4200, (b) Ta=4300, and (c) Ta=4400

Figure 12

Growth rate of the relative flow intensity in the axial direction with respect to the Taylor number (Da=10−5, a¯=0.74375, b¯=0.95, L=5, and ϕ=0.25)

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